Question

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Explanation:

Step1: Identify like terms

The given polynomial has terms $8x^3y^2$, $3xy^2$, $-4y^3$. A fully simplified polynomial has no like terms, so we need a term that cannot combine with any existing term.

Step2: Analyze each option

• $7x^0y^3 = 7y^3$: This is like $-4y^3$, so they would combine, leaving a non-simplified intermediate form.
• $x^3y^3$: No existing term has the same exponents for $x$ and $y$ (degree $6$, with $x^3,y^3$).
• $x^2y^2$: No existing term has $x^2y^2$, but let's check the last option.
• $7xy^2$: This is like $3xy^2$, so they would combine to $10xy^2$.

Step3: Confirm valid term

Only $x^3y^3$ does not have a like term in the given polynomial, so adding it keeps the polynomial fully simplified in standard form.

Answer:

$x^3y^3$